E225C – Lecture 16 OFDM Introduction
EE225C

Introduction to OFDM l Basic idea
» Using a large number of parallel narrow-band subcarriers instead of a single wide-band carrier to transport information

l

Advantages
» Very easy and efficient in dealing with multi-path » Robust again narrow-band interference

l

Disadvantages
» Sensitive to frequency offset and phase noise » Peak-to-average problem reduces the power efficiency of RF amplifier at the transmitter

l

Adopted for various standards
– DSL, 802.11a, DAB, DVB

1

Multipath can be described in two domains: time and frequency
Time domain: Impulse response

time

time time Impulse response

Frequency domain: Frequency response time time

time Sinusoidal signal as input

f Frequency response

time Sinusoidal signal as output

Modulation techniques: monocarrier vs. multicarrier
Channel Channelization Guard bands N carriers Similar to FDM technique B Pulse length ~ N/B – Data are shared among several carriers and simultaneously transmitted Advantages Furthermore – Flat Fading per carrier – N long pulses – ISI is comparatively short – N short EQs needed – Poor spectral efficiency because of band guards – It is easy to exploit Frequency diversity – It allows to deploy 2D coding techniques – Dynamic signalling

B Pulse length ~1/B – Data are transmited over only one carrier

Drawbacks – Selective Fading – Very short pulses – ISI is compartively long – EQs are then very long – Poor spectral efficiency because of band guards

To improve the spectral efficiency: Eliminate band guards between carriers To use orthogonal carriers (allowing overlapping)

2

Orthogonal Frequency Division Modulation
N carriers
Symbol: 2 periods of f0

Transmit f
B
Symbol: 8 periods of f0

+
Symbol: 4 periods of f0

f

Data coded in frequency domain Transformation to time domain: each frequency is a sine wave in time, all added up.

Channel frequency response

Decode each frequency bin separately Receive time f B Time-domain signal Frequency-domain signal

OFDM uses multiple carriers to modulate the data
Time-frequency grid Frequency N carriers Data

B f0

Carrier

B Features – No intercarrier guard bands – Controlled overlapping of bands – Maximum spectral efficiency (Nyquist rate) – Easy implementation using IFFTs – Very sensitive to freq. synchronization Modulation technique A user utilizes all carriers to transmit its data as coded quantity at each frequency carrier, which can be quadrature-amplitude modulated (QAM). T=1/f0 One OFDM symbol Time

Intercarrier Separation = 1/(symbol duration)

3

OFDM Modulation and Demodulation using FFTs d0 b0 d1 P/S IFFT b1 d2 d0, d1, d2, …., dN-1 b2 Inverse fast d3 Parallel to . Fourier transform . serial converter . Transmit time-domain . f . samples of one symbol . . . time bN-1 dN-1 Data coded in Data in time domain: frequency domain: one symbol at a time one symbol at a time Decode each b0’ frequency bin b1’ independently b2’ . . f . . bN-1’

d0’, d1’, …., dN-1’

S/P
Serial to parallel converter

Receive time-domain samples of one symbol

time

d0’ d1’ d2’ . . . . dN-1’

FFT
Fast Fourier transform

Loss of orthogonality (by frequency offset)
Transmission pulses Reception pulse with offset δ ψ k (t) = exp( jk 2π t / T ) y ψ k +m ( t) = exp ( j2π (k + m )t / T )

ψ k+ m (t) = exp ( j2π (k + m + δ ) / T ) con δ ≤ 1 / 2 δ Interference between channels k and k+m

I m (δ ) = ∫ exp( jk2πt / T ) exp(− j(k + m + δ )2πt / T )dt =
T 0

T ( − exp(− j2πδ )) 1 j 2π(m + δ )

I m (δ) =

T sin πδ π m+δ

Summing up ∀m

∑I m 2 m

(δ ) ≈ (Tδ)2 ∑ m= 1

N− 1

1 23 ≈ (Tδ )2 14 m2

for

N >> 1 (N > 5

Is enough )

0 Interference: Im(? )/T en dB -10 -20 -30 -40 -50 -60 -70 -0.4

Loss for 8 carriers m=1 m=3 m=5 m=7

Total ICI due to loss of orthogonality
-10 -15 δ =0.05 -20 -25 δ =0.02 -30 δ =0.01 -35 δ =0.005 -40 Practical -45 δ =0.002 δ assumed r.v. -50 δ =0.001 Gaussian σ=δ -55 -60 2 4 6 8 10 12 14 16 Carrier position within the band (N=16)
ICI in dB

limit

Asymetric
-0.3 -0.2 -0.1 0.1 Frequency offset: ∂
0

0.2

0.3

0.4

4

Loss of orthogonality (time)
Let us assume a misadjustment τ
Xi = c 0 ∫
− T /2+ τ −T /2

ψ k (t )ψ l (t − τ )dt + c 1 ∫
*

T/ 2

−T / 2+τ

ψ k (t )ψ l (t − τ )dt
*

2 consecutive symbols

Then if m=k-l

τ  senmπ 2 T T , c ≠c 0 1 Xi =  mπ  0, c0 = c1 
X 2 E i2  T

Or approximately, when τ